Yes, the original 7.92x57 (8mm Mauser) was designated J or JR, and is .318 . It was originally a round nose bullet. The "modernized" cartridge used a spitzer bullet, is designated JS, and is .323 .
I would not want to shoot the larger .323 in a smaller .318 bore. And shooting a .318 bullet in a .323 bore would be ok, but likely inaccurate.
Dan

For years the round was called the 8 X 57 "J"S - actually still is. So what does the "J" stand for? All sorts of theories.

Relatively recent research indicates that the German designation was the 8 X 57 "I" S - but when the name was converted to English, it became "J" because the German capital "I" looks like an English "J" - and at the time, due to the "Great War" no one really cared about the details. (This info is in Wikipedia, but I already knew it, so no cribbing Wiki).

The "I" "S" is "infantry" "Spitzer", "spitzer" is a shortened form of the German word for "pointed." Even though incorrect, the "J" usage has carried on for over 100 years.